The average of the marks obtained in an examination by 8 students was 51 and by 9 other students was 68. The average marks of all 17 students was:

Options

A. 59
B. 59.5
C. 60
D. 60.5

Answer

To find the average marks of all 17 students, we will follow these steps:

### Step 1: Calculate the total marks of the first group of students
The average marks of the first group of 8 students is given as 51. To find the total marks obtained by these students, we can use the formula:

\[ \text{Total Marks} = \text{Average} \times \text{Number of Students} \]

For the first group:

\[ \text{Total Marks of 8 students} = 51 \times 8 = 408 \]

### Step 2: Calculate the total marks of the second group of students
The average marks of the second group of 9 students is given as 68. Similarly, we calculate the total marks for this group:

\[ \text{Total Marks of 9 students} = 68 \times 9 = 612 \]

### Step 3: Calculate the total marks of all students
Now, we can find the total marks of all 17 students by adding the total marks of both groups:

\[ \text{Total Marks of all 17 students} = \text{Total Marks of 8 students} + \text{Total Marks of 9 students} \]

\[ \text{Total Marks of all 17 students} = 408 + 612 = 1020 \]

### Step 4: Calculate the average marks of all 17 students
Finally, we can find the average marks of all 17 students using the formula:

\[ \text{Average} = \frac{\text{Total Marks}}{\text{Number of Students}} \]

\[ \text{Average of all 17 students} = \frac{1020}{17} = 60 \]

### Final Answer
The average marks of all 17 students is **60**.

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